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Proof step 814 from proof hasSharing-put-index-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), hasSharing(r, st[r0 -- i ', refval(r2)]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = r2, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ hasSharing(r, st) ↔ (∃ sks1, sks2. fits(r, sks1, st) ∧ fits(r, sks2, st) ∧ sks1 ≠ sks2 ∧ sks1 ≠ [] ∧ sks2 ≠ [] ∧ st[r -- sks1] .refval ≠ jvmref ∧ st[r -- sks1] = st[r -- sks2])
Proof step 813:
st[r0 -- _type] .type = mkarraytype(ty), ∃ sks1, sks2. fits(r, sks1, st[r0 -- i ', refval(r2)]) ∧ fits(r, sks2, st[r0 -- i ', refval(r2)]) ∧ sks1 ≠ sks2 ∧ sks1 ≠ [] ∧ sks2 ≠ [] ∧ (st[r0 -- i ', refval(r2)][r -- sks1]) .refval ≠ jvmref ∧ (st[r0 -- i ', refval(r2)][r -- sks1]) = (st[r0 -- i ', refval(r2)][r -- sks2]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = r2, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: hasSharing-def antecedent: succedent: hasSharing(r, st) ↔ (∃ sks1, sks2. fits(r, sks1, st) ∧ fits(r, sks2, st) ∧ sks1 ≠ sks2 ∧ sks1 ≠ [] ∧ sks2 ≠ [] ∧ st[r -- sks1] .refval ≠ jvmref ∧ st[r -- sks1] = st[r -- sks2]) substlist: [st, r] → [st[r0 -- i ', refval(r2)], r] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- i ', refval(r2)], r)]]